Modular groups and planar maps
Number Theory
2020-10-06 v2 Algebraic Geometry
Group Theory
Abstract
In this paper we give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free and a formula for their conjugacy classes. We do so by exhibiting a correspondence between these groups and the trivalent maps on a sphere. We focus on the particular case of the subgroups of index 18 which have some interesting geometric properties.
Cite
@article{arxiv.1910.03050,
title = {Modular groups and planar maps},
author = {Abdellah Sebbar and Khalil Besrour},
journal= {arXiv preprint arXiv:1910.03050},
year = {2020}
}
Comments
Few typos have been corrected in the references